You can easily spend one day wandering around the downtown area. There are several museums and the area is small enough that you can easily walk. The national museum, just east of downtown, is interesting. There is a butterfly garden in it and a decent sized tourist market beside it if you need to do souvenier shopping. The Gold Museum is also interesting - its underground - the deeper you go the more interesting it becomes. Get a map - your hotel may have one or you can download one. Be warned - most streets don't have street signs so you have to go by landmarks. If you are concerned about getting lost take a business card from the hotel or write down the address and you can take a taxi back if you need to. Taxis are supposed to use a meter in San Jose but not all will.

If you want to visit one of the volcanoes, Poas or Irazu are popular ones, you may want to sign up for a tour before you get there. Most of the companies will pick you up at your hotel. The earlier you leave the better, as clouds tend to come in by mid-morning. There are also coffee plantation tours and a nature reserve. A lot of the tours tend to combine one or two activities.

You can google "things to do around San Jose, Costa Rica" and you will have more options than you can possibly consider. If you get a hold of G Adventures they may be able to arrrange something for you as well.